It is well known that the CLR inequality implies the Lieb-Thirring inequalities [1]}, [2]} for the Riesz means of negative eigenvalues of Schrödinger operators (see, e.g., [3]}), although this does not lead to the best bounds for the best constants of these inequalities. Likewise, as a consequence of the CLR inequalities provided by Theorem REF  we shall obtain the following version of the Lieb-Thirring inequalities for NC tori.
